Distance-redshift and growth-redshift relations as two windows on acceleration and gravitation: Dark energy or new gravity?

Small distortions in the observed shapes of distant galaxies, a cosmic shear due to gravitational lensing, can be used to simultaneously determine the distance-redshift relation, $r(z)$, and the density contrast growth factor, $g(z)$. Both of these functions are sensitive probes of the acceleration. Their simultaneous determination allows for a consistency test and provides sensitivity to physics beyond the standard dark energy paradigm.